A Turbocharger is a small compressor driven by the engine's exhaust gases which increases power. Unlike a supercharger which is driven by a belt off the engine to increase power. A Turbocharger is used to increase the power output of a car by increasing the mass of oxygen entering the engine - essentially by cramming more air into the engine, more fuel can burn and hence more power can be given per cycle.
The biggest advantage of turbochargers is their considerable low weight and cost and given the excellent performance increase they are used widely. However aftermarket turbo kits can cause damange to a vehicles engine depending on the setup.
An alternative to the turbocharger and the supercharger is to use a multivalve engine, where more valves than the traditional two per cylinder move air and fuel through the engine more quickly. Nevertheless performance cars have multivalves AND turbochargers.